For a polynomial f defined over a number field K, when replacing K by its absolute field L = K.absolute_field(names='b') there might be an error when changing f with the appropriate isomorphism f.change_ring(L.structure()[1]).

The problem arises from the fact that change_ring wants to check whether the isomorphism is part of K.Hom(L) by calling K.Hom(L)(L.structure()[1]) which gives an error if L.structure()[1] is not an instance of NumberFieldHomomorphism_im_gens which it not necessarily is. Here is a minimal working example

sage: K.<a> = CyclotomicField(8)
sage: L.<b> = K.absolute_field()
sage: phi = L.structure()[1]
sage: phi.parent() == K.Hom(L)
True
sage: K.Hom(L)(phi)
Traceback (most recent call last):
...
TypeError: unable to convert Isomorphism given by variable name change map:
  From: Cyclotomic Field of order 8 and degree 4
  To:   Number Field in b with defining polynomial x^4 + 1 to an element of Number Field in b with defining polynomial x^4 + 1

The error seems a consequence of a call to K.Hom(L) interpreting the argument as an element of the codomain if it is not an instance of NumberFieldHomomorphism_im_gens.

Here is the example failing on change_ring where the error message is even less insightful

sage: K.<a> = CyclotomicField(8)
sage: L.<b> = K.absolute_field()
sage: R.<x> = K[]
sage: f = x^2 + a
sage: f.change_ring(L.structure()[1])
Traceback (most recent call last):
...
TypeError: 

Depends on #29008
Depends on #29010

Component: number fields

Keywords: absolute field

Author: Peter Bruin

Branch/Commit: 5939e98

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/28869